The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A306880 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
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A306880

Expansion of e.g.f. (sec(x) + tan(x))/(1 + LambertW(-x)).
(history; published version)

#27 by Alois P. Heinz at Sat Jun 11 20:18:44 EDT 2022

STATUS

proposed

approved

#26 by Chai Wah Wu at Sat Jun 11 16:58:42 EDT 2022

STATUS

editing

proposed

#25 by Chai Wah Wu at Sat Jun 11 16:58:37 EDT 2022

PROG

(Python)

from itertools import accumulate, count, islice

def A306880_gen(): # generator of terms

blist = tuple()

for i in count(0):

yield (blist := tuple(accumulate(reversed(blist), initial=i**i)))[-1]

A306880_list = list(islice(A306880_gen(), 30)) # Chai Wah Wu, Jun 11 2022

STATUS

approved

editing

#24 by Vaclav Kotesovec at Sat Aug 17 03:32:34 EDT 2019

STATUS

editing

approved

#23 by Vaclav Kotesovec at Sat Aug 17 03:32:28 EDT 2019

FORMULA

a(n) ~ (1 + sin(exp(-1)))/cos(exp(-1)) * n^n. - Vaclav Kotesovec, Aug 17 2019

STATUS

approved

editing

#22 by Susanna Cuyler at Tue Apr 16 21:41:25 EDT 2019

STATUS

proposed

approved

#21 by Ilya Gutkovskiy at Tue Apr 16 18:25:40 EDT 2019

STATUS

editing

proposed

#20 by Ilya Gutkovskiy at Tue Apr 16 17:58:45 EDT 2019

CROSSREFS

Cf. A000111, A000312, A306881.

#19 by Ilya Gutkovskiy at Tue Apr 16 17:54:11 EDT 2019

NAME

allocated for Ilya Gutkovskiy

Expansion of e.g.f. (sec(x) + tan(x))/(1 + LambertW(-x)).

DATA

1, 2, 7, 44, 401, 4796, 70783, 1240448, 25146113, 578583952, 14892958551, 423979878816, 13225810908881, 448604790288448, 16437893908228367, 647074747622534912, 27233273311687115649, 1220273444664347994368, 57998633082360310382119, 2914426113026062106334720, 154378135436424206699590545

OFFSET

0,2

COMMENTS

Boustrophedon transform of A000312.

LINKS

<a href="/index/Bo#boustrophedon">Index entries for sequences related to boustrophedon transform</a>

MATHEMATICA

nmax = 20; CoefficientList[Series[(Sec[x] + Tan[x])/(1 + LambertW[-x]), {x, 0, nmax}], x] Range[0, nmax]!

t[n_, 0] := If[n < 1, 1, n^n]; t[n_, k_] := t[n, k] = t[n, k - 1] + t[n - 1, n - k]; a[n_] := t[n, n]; Array[a, 21, 0]

CROSSREFS

Cf. A000111, A000312.

KEYWORD

allocated

nonn

AUTHOR

Ilya Gutkovskiy, Apr 16 2019

STATUS

approved

editing

#18 by Ilya Gutkovskiy at Tue Apr 16 17:54:11 EDT 2019

NAME

allocated for Ilya Gutkovskiy

KEYWORD

recycled

allocated